Second, we discuss the features of electron distribution functions possibly modified by resonant interaction with the previously discussed LHW.
This resonant wave-particle interaction accelerates sub-thermal electrons (with speed \(v_z \lessapprox v_{the}\) ) to supra-thermal energies (with speed \(v_z \gtrapprox 2v_{the}\) ) in the direction parallel to the ambient magnetic field, as shown in Fig. REF  top panels.
In the following we assume an unperturbed electron temperature of 50 eV (typical values at Mercury's magnetopause being \(\sim 20-100\)  eV [1]}).
This acceleration process is well in the range of observations of the electron instrument MPPE/MEA onboard the Mio spacecraft of the BepiColombo mission [2]}, since this instrument includes two electron analyzers that can measure the three-dimensional energy distribution of electrons in the range 3-3000 eV (in solar wind mode) or 3-25500 eV (in magnetospheric mode), with a time resolution of 1 second [3]}.
Here, we simulate the instrumental response of MPPE/MEA when encountering electrons accelerated by a LHDI at Mercury's magnetopause, as shown in Fig. REF , with the unperturbed electron distribution function in blue, and the one resulting from interaction with LHDI at long times in red.
In Fig. REF , the uncertainties on the simulated response of the sensor MEA are obtained using the uncertainty on the G-factor of the instrument reported in [2]} (of the order of 10%).
So, on the one hand we predict that the modifications in the electron distribution function above 100 eV are observable by MPPE/MEA in the case of a strongly inhomogeneous magnetopause (width around one ion gyro-radius, or less), as shown in the left panel of Fig. REF .
On the other hand, since this process is very sensitive to the width of the magnetopause layer, we expect negligible modifications in the electron distribution function for less inhomogeneous magnetopause conditions (width around two ion gyro-radii or more), as shown in the right panel of Fig. REF .
With typical magnetic field and temperature values at Mercury's magnetopause the ion gyroradius is around \(20-80\)  km.
